Finite Group Databasebeta

← C13×#13329 #15699668

Subgroups — C13×#13329 #15699668

Order 3328.

578 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×Q32C211yesmaximal, characteristic, complemented
2C22×C13×SD32C211yesmaximal, characteristic
3C2×C13×#495C211yesmaximal, characteristic
4C2×C13×#358C211yesmaximal, characteristic, complemented
5C2×C13×#357C211yesmaximal, characteristic
6C13×#1969C211yesmaximal, characteristic, complemented
7C13×#1374C211yesmaximal, characteristic, complemented
8C22×C13×Q16C2211yescharacteristic
9C22×C13×Q16C2211yescharacteristic
10C22×C13×SD16—21no—
11C22×C13×D8C2211yescharacteristic
12C2×C13×#124—21no—
13C2×C13×Q32—22no—
14C2×C13×Q32—22no—
15C2×C13×Q32—22no—
16C2×C13×SD32—22no—
17C2×C13×SD32—22no—
18C2×C13×SD32—22no—
19C22×C13×C16C2211yescharacteristic
20C22×C13×C16C2211yescharacteristic
21C13×#495—22no—
22C13×#495—22no—
23C2×C13×#107C2211yescharacteristic
24C2×C13×#103—21no—
25C2×C4×C8×C13C2211yescharacteristic
26C13×#391—21no—
27C13×#358—22no—
28C13×#357—22no—
29C22×Q8×C13—21no—
30C22×Q8×C13—21no—
31C22×D4×C13—21no—
32C2×C13×Q16—21no—
33C2×C13×Q16—21no—
34C2×C13×Q16—21no—
35C2×C13×Q16—21no—
36C2×C13×Q16—21no—
37C2×C13×Q16—21no—
38C2×C13×Q16—21no—
39C2×C13×Q16—21no—
40C2×C13×Q16—21no—
41C2×C13×Q16—21no—
42C2×C13×Q16D412yes—
43C2×C13×Q16D412yes—
44C2×C13×SD16—24no—
45C2×C13×SD16—42no—
46C2×C13×SD16—42no—
47C2×C13×D8—21no—
48C2×C13×D8—21no—
49C2×C13×D8—21no—
50C2×C13×D8—21no—
51C2×C13×D8—21no—
52C2×C13×D8D412yes—
53C22×C8×C13D411yescharacteristic
54C22×C8×C13C2311yescharacteristic
55C13×#124—24no—
56C13×#124—42no—
57C2×C13×C4⋊C4—21no—
58C2×C13×C22⋊C4—42no—
59C2×C42×C13D411yescharacteristic
60C13×Q32—28no—
61C13×SD32—28no—
62C2×C13×C16—21no—
63C2×C13×C16—21no—
64C2×C13×C16—21no—
65C2×C13×C16—21no—
66C2×C13×C16D412yes—
67C2×C13×C16D412yes—
68C13×#107—21no—
69C13×#107—21no—
70C13×#103—42no—
71C4×C8×C13—21no—
72C4×C8×C13—21no—
73C13×#95—42no—
74#13329C1311yesmaximal, characteristic, direct product factor, Sylow
75C24×C13—41no—
76C2×Q8×C13—22no—
77C2×Q8×C13—22no—
78C2×Q8×C13—41no—
79C2×Q8×C13—41no—
80C2×Q8×C13—41no—
81C2×Q8×C13—41no—
82C2×Q8×C13—41no—
83C2×Q8×C13—41no—
84C2×Q8×C13—41no—
85C2×Q8×C13—41no—
86C2×Q8×C13—41no—
87C2×Q8×C13—41no—
88C2×D4×C13—22no—
89C2×D4×C13—41no—
90C2×D4×C13—41no—
91C2×D4×C13—41no—
92C2×D4×C13—41no—
93C2×D4×C13—41no—
94C22×C4×C13—41no—
95C22×C4×C13—41no—
96C22×C4×C13—41no—
97C22×C4×C13D812yes—
98C22×C4×C13C2×D411yescharacteristic
99C13×Q16—22no—
100C13×Q16—22no—
101C13×Q16—22no—
102C13×Q16—22no—
103C13×Q16—41no—
104C13×Q16—41no—
105C13×Q16—41no—
106C13×Q16—41no—
107C13×SD16—48no—
108C13×D8—22no—
109C13×D8—22no—
110C13×D8—41no—
111C13×D8—41no—
112C2×C8×C13—21no—
113C2×C8×C13—21no—
114C2×C8×C13D812yes—
115C2×C8×C13C2×D411yescharacteristic
116C2×C8×C13C2×D411yescharacteristic
117C2×C8×C13C2×D411yescharacteristic
118C2×C8×C13C2×D411yescharacteristic
119C2×C8×C13C2×D411yescharacteristic
120C2×C8×C13#4111yescharacteristic
121C13×C4⋊C4—41no—
122C13×C4⋊C4—41no—
123C13×C22⋊C4—48no—
124C42×C13—21no—
125C42×C13—21no—
126C13×C16—22no—
127C13×C16—22no—
128C22×Q32C2×C1311yescharacteristic, complemented
129C22×SD32C2×C1311yescharacteristic
130C2×#495C2×C1311yescharacteristic
131C2×#358C2×C1311yescharacteristic, complemented
132C2×#357C2×C1311yescharacteristic
133#1969C2×C1311yescharacteristic, complemented
134#1374C2×C1311yescharacteristic, complemented
135C23×C13—42no—
136C23×C13—81no—
137C23×C13—81no—
138C23×C13—82no—
139C23×C13—82no—
140C23×C13C2×D811yescharacteristic
141Q8×C13—42no—
142Q8×C13—42no—
143Q8×C13—42no—
144Q8×C13—42no—
145Q8×C13—81no—
146Q8×C13—81no—
147Q8×C13—81no—
148Q8×C13—81no—
149D4×C13—42no—
150D4×C13—42no—
151D4×C13—81no—
152D4×C13—81no—
153C2×C4×C13—22no—
154C2×C4×C13—22no—
155C2×C4×C13—22no—
156C2×C4×C13—42no—
157C2×C4×C13—42no—
158C2×C4×C13—81no—
159C2×C4×C13—81no—
160C2×C4×C13—81no—
161C2×C4×C13—81no—
162C2×C4×C13—81no—
163C2×C4×C13—82no—
164C2×C4×C13#12011yescharacteristic
165C2×C4×C13#12111yescharacteristic
166C2×C4×C13#12711yescharacteristic
167C2×C4×C13C2×D811yescharacteristic
168C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
170C8×C13—22no—
171C8×C13#12011yescharacteristic
172C8×C13#12011yescharacteristic
173C8×C13#12111yescharacteristic
174C8×C13#12111yescharacteristic
175C22×Q16C22×C1311yescharacteristic
176C22×Q16C22×C1311yescharacteristic
177C22×SD16—21no—
178C22×D8C22×C1311yescharacteristic
179C2×#124—21no—
180C2×Q32—22no—
181C2×Q32—22no—
182C2×Q32—22no—
183C2×SD32—22no—
184C2×SD32—22no—
185C2×SD32—22no—
186C22×C16C22×C1311yescharacteristic
187C22×C16C22×C1311yescharacteristic
188#495—22no—
189#495—22no—
190C2×#107C22×C1311yescharacteristic
191C2×#103—21no—
192C2×C4×C8C22×C1311yescharacteristic
193#391—21no—
194#358—22no—
195#357—22no—
196C22×C13—84no—
197C22×C13—82no—
198C22×C13—162no—
199C22×C13—161no—
200C22×C13—161no—
201C22×C13#44711yescharacteristic
202C22×C13#45911yescharacteristic
203C22×C13#49311yescharacteristic
204C22×C13#50812yes—
205C22×C13#51012yes—
206C4×C13—42no—
207C4×C13—82no—
208C4×C13—82no—
209C4×C13—161no—
210C4×C13#39211yescharacteristic
211C4×C13#44711yescharacteristic
212C4×C13#45911yescharacteristic
213C4×C13#49611yescharacteristic
214C22×Q8—21no—
215C22×Q8—21no—
216C22×D4—21no—
217C2×Q16—21no—
218C2×Q16—21no—
219C2×Q16—21no—
220C2×Q16—21no—
221C2×Q16—21no—
222C2×Q16—21no—
223C2×Q16—21no—
224C2×Q16—21no—
225C2×Q16—21no—
226C2×Q16—21no—
227C2×Q16D4×C1312yes—
228C2×Q16D4×C1312yes—
229C2×SD16—24no—
230C2×SD16—42no—
231C2×SD16—42no—
232C2×D8—21no—
233C2×D8—21no—
234C2×D8—21no—
235C2×D8—21no—
236C2×D8—21no—
237C2×D8D4×C1312yes—
238C22×C8D4×C1311yescharacteristic
239C22×C8C23×C1311yescharacteristic
240#124—24no—
241#124—42no—
242C2×C4⋊C4—21no—
243C2×C22⋊C4—42no—
244C2×C42D4×C1311yescharacteristic
245Q32—28no—
246SD32—28no—
247C2×C16—21no—
248C2×C16—21no—
249C2×C16—21no—
250C2×C16—21no—
251C2×C16D4×C1312yes—
252C2×C16D4×C1312yes—
253#107—21no—
254#107—21no—
255#103—42no—
256C4×C8—21no—
257C4×C8—21no—
258#95—42no—
259C2×C13—162no—
260C2×C13#201111yescharacteristic
261C2×C13#218912yes—
262C2×C13#221112yes—
263C2×C13#224911yescharacteristic
264C2×C13#225111yescharacteristic
265C24—41no—
266C2×Q8—22no—
267C2×Q8—22no—
268C2×Q8—41no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×D4—22no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—41no—
282C2×D4—41no—
283C2×D4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4C13×D812yes—
288C22×C4C2×D4×C1311yescharacteristic
289Q16—22no—
290Q16—22no—
291Q16—22no—
292Q16—22no—
293Q16—41no—
294Q16—41no—
295Q16—41no—
296Q16—41no—
297SD16—48no—
298D8—22no—
299D8—22no—
300D8—41no—
301D8—41no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8C13×D812yes—
305C2×C8C2×D4×C1311yescharacteristic
306C2×C8C2×D4×C1311yescharacteristic
307C2×C8C2×D4×C1311yescharacteristic
308C2×C8C2×D4×C1311yescharacteristic
309C2×C8C2×D4×C1311yescharacteristic
310C2×C8C13×#4111yescharacteristic
311C4⋊C4—41no—
312C4⋊C4—41no—
313C22⋊C4—48no—
314C42—21no—
315C42—21no—
316C16—22no—
317C16—22no—
318C13#1332911yescharacteristic, direct product factor, Sylow
319C23—42no—
320C23—81no—
321C23—81no—
322C23—82no—
323C23—82no—
324C23C2×C13×D811yescharacteristic
325Q8—42no—
326Q8—42no—
327Q8—42no—
328Q8—42no—
329Q8—81no—
330Q8—81no—
331Q8—81no—
332Q8—81no—
333D4—42no—
334D4—42no—
335D4—81no—
336D4—81no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—82no—
348C2×C4C13×#12011yescharacteristic
349C2×C4C13×#12111yescharacteristic
350C2×C4C13×#12711yescharacteristic
351C2×C4C2×C13×D811yescharacteristic
352C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
353C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
354C8—22no—
355C8C13×#12011yescharacteristic
356C8C13×#12011yescharacteristic
357C8C13×#12111yescharacteristic
358C8C13×#12111yescharacteristic
359C22—82no—
360C22—84no—
361C22—161no—
362C22—161no—
363C22—162no—
364C22C13×#44711yescharacteristic
365C22C13×#45911yescharacteristic
366C22C13×#49311yescharacteristic
367C22C13×#50812yes—
368C22C13×#51012yes—
369C4—42no—
370C4—82no—
371C4—82no—
372C4—161no—
373C4C13×#39211yescharacteristic
374C4C13×#44711yescharacteristic
375C4C13×#45911yescharacteristic
376C4C13×#49611yescharacteristic
377C2—162no—
378C2C13×#201111yescharacteristic
379C2C13×#218912yes—
380C2C13×#221112yes—
381C2C13×#224911yescharacteristic
382C2C13×#225111yescharacteristic
subgroupG/H
center, socleC23×C13C2×D8
commutator, Frattini, cosocleC22×C8C23×C13
prime radicalC22×C13×D8C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C13 ◁ C2×C42×C13 ◁ C2×C4×C8×C13 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×C13×Q32C2semidirect
4. C2×C13×#358C2semidirect
6. C13×#1969C2semidirect
7. C13×#1374C2semidirect
74. #13329C13direct (N × H)
128. C22×Q32C2×C13semidirect
131. C2×#358C2×C13semidirect
133. #1969C2×C13semidirect
134. #1374C2×C13semidirect
318. C13#13329direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C13×Q322
C22×C13×SD322
C2×C13×#4952
C2×C13×#3582
C2×C13×#3572
C13×#19692
C13×#13742
#1332913